Question: The grades on a math midterm at Almond are normally distributed with $\mu = 70$ and $\sigma = 2.0$. Brandon earned a $67$ on the exam. Find the z-score for Brandon's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Brandon's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{67 - {70}}{{2.0}}} $ ${ z \approx -1.50}$ The z-score is $-1.50$. In other words, Brandon's score was $1.50$ standard deviations below the mean.